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Abstract:

The spatial rigidity and strength of precast multi-story buildings are largely determined by the rigidity of the shear bonds connecting the vertical load-bearing reinforced concrete structures. When a horizontal load is applied in asymmetrical in-plan load-bearing systems of multi-story buildings, torsion occurs. In vertical shear bonds, especially those located furthest from the center of rigidity, a torque appears. This article presents the results of experimental studies of welded joints of precast buildings under the action of shear and torsion. The research study has been conducted using full-scale samples of shear bonds. The samples have been loaded with a static load vertical shear force and horizontal torsion moment. Various loading conditions are considered. Deformation diagrams of shear bonds were obtained. The limit state of a welded joint under shear and shear with torsion is described. The obtained experimental data on the rigidity of shear connections can be used in mathematical models for determining the stress-strain state of load-bearing systems of panel multi-story buildings.

Keywords:

Welded joints,Shear bonds,Torsion,Panel buildings,Stress-strain state,

Refference:

I. Ajay T., Parthasarathi N., Prakash M., : ‘Effect of planar irregularity of linear static and dynamic analysis’. Materials Today: Proceedings. Vol. 40, 2020. 10.1016/j.matpr.2020.03.499
II. Benaied B., Hemsas M., Benanane A., Hentri M., : ‘Seismic analysis of RC building frames with vertical mass and stiffness irregularities using adaptive pushover analysis’. Revista De La Construcción. Vol. 22(3), pp. 597–612, 2023. 10.7764/RDLC.22.2.597
III. Benavent-Climent A., Morillas L., Escolano-Margarit D., : ‘Inelastic torsional seismic response of nominally symmetric reinforced concrete frame structures: Shaking table tests’. Engineering Structures. Vol. 80, pp. 109–117, 2014. 10.1016/j.engstruct.2014.08.047
IV. Botis M., Cerbu С. A., : ‘Method for Reducing of the Overall Torsion for Reinforced Concrete Multi-Storey Irregular Structures’. Applied Sciences. Vol. 10, 5555, 2020. 10.3390/app10165555
V. De Stefano M., Pintucchi B., :‘A review of research on seismic behaviour of irregular building structures since 2002’. Bull Earthquake Eng. Vol. 6, pp. 285–308, 2008. 0.1007/s10518-007-9052-3
VI. Drozdov P., : ‘Design and Calculation of Load-bearing Systems of Multistorey Buildings and their Elements’. Moscow. Stroyizdat, 1977.
VII. Hussein G., Eid N., Khaled H., : ‘Torsional Behavior of Irregular Structures during Earthquakes’. Journal of Mechanical and Civil Engineering. Vol. 16, pp. 40-55, 2019. 10.9790/1684-1605044055
VIII. Karyakin A.A., Derbentsev I.S., Tarasov M.V., : ‘Experimental and Numerical Research on Tensile Performance of Inter-Panel Fastener Joints of Large-Panel Buildings’. IOP Conf. Ser.: Mater. Sci. Eng. Vol. 262, 2017. 10.1088/1757-899X/262/1/012046
IX. Khatiwada P., Lumantarna E., : ‘Simplified Method of Determining Torsional Stability of the Multi-Storey Reinforced Concrete Buildings’. Civil Eng. Vol. 2, pp. 290–308, 2021. 10.3390/civileng2020016
X. Lim H., Kang J. W., Pak H., Chi H., Lee Y. and Kim J., : ‘Seismic Response of a Three-Dimensional Asymmetric Multi-Storey Reinforced Concrete Structure’. Applied Sciences. Vol. 8(4), 479, 2018. 10.3390/app8040479
XI. Lyublinskiy V., Struchkov V., : ‘Resistance of Vertical Joints During Torsion of Multistorey Buildings’, Proceedings of FORM 2022, LNCE, Springer. Vol. 282, pp. 407-415, 2023. 10.1007/978-3-031-10853-2_38
XII. Lyublinskiy V.A., : ‘To the question of redistribution of stress in Vertical bearing rc structures multi-story buildings’. Building structures. Vol. 2 (94), pp. 39-45, 2021. 10.33979/2073-7416-2021-94-2-39-45
XIII. Lyublinskiy V.A., Tomina M.V., : ‘Experimental study of the strength and suppleness of a vertical welded joint’. Syst. Meth.Techn. Vol. 3(39), pp. 154-158, 2018. 10.18324/2077-5415-2018-3-154-158
XIV. Manual for the calculation of large-panel buildings Issue 1 Characteristics of the rigidity of walls, elements and joints of large-panel buildings. Moscow. Stroyizdat, 1974.
XV. Nabila Rossley, Farah Nora Aznieta Abdul Aziz, Heng Chiang Chew, Nima Farzadnia., : ‘Behaviour of vertical loop bar connection in precast wall subjected to shear load’. Aust. J. Basic & Appl. Sci. Vol. 8(1), pp. 370-380, 2014.
XVI. Naresh kumar B. G., Punith N., Bhyrav R.B., Arpitha T. P., : ‘Assessment of Location of Centre of Mass and Centre of Rigidity for Different Setback Buildings’. International Journal of Engineering Research & Technology. Vol. 6, Issue 5, pp. 801-804, 2017. 10.17577/IJERTV6IS050488
XVII. Negro P., Mola E., Molina F.J., Magonette G., : ‘Full-scale PsD testing of a torsionally unbalanced three-storey non-seismic RC frame’. Proceedings of 13th world conference on earthquake engineering, Vancouver, Canada; 2004.
XVIII. Satheesh A.J., Jayalekshmi B.R., Venkataramana Ka., : ‘Effect of in-plan eccentricity on vertically stiffness irregular buildings under earthquake loading’. Soil Dynamics and Earthquake Engineering. Vol. 137, 106251, 2020. 10.1016/j.soildyn.2020.106251
XIX. Sharma J., Singh A., Sehgal R., : ‘Torsional Reduction Techniques in High Rise Structures’. International Journal of Engineering Research & Technology (IJERT). Vol. 3, Issue 10, 2015. 10.17577/IJERTCONV3IS10013
XX. Shen S.D., Pan P., Miao Q.S., Li W.F., Gong R.H., : ‘Test and analysis of reinforced concrete (RC) precast shear wall assembled using steel shear key (SSK)’. Earthq. Eng. Struct. Dyn. Vol. 48, pp. 1595–1612, 2019. 10.1002/eqe.3215
XXI. Shuvalov A., Gorbunov I., Kovalev M., Faizova A., : ‘Experimental studies of compliance of vertical joints used in construction of high-rise panel buildings’, MATEC Web of Conferences, Vol. 196, 02049, 2018. 10.1051/matecconf/201819602049
XXII. Singhal S., Chourasia A., Chellappa S., Parashar J., : ‘Precast reinforced concrete shear walls: State of the art review’. Struct. Concr. Vol. 20, pp. 886–898, 2019. 10.1002/suco.201800129
XXIII. Sritharan S., Aaleti S., Henry R.S., Liu K.Y., Tsai K.C., : ‘Precast concrete wall with end columns (PreWEC) for earthquake resistant design’. Earthq. Eng. Struct. Dyn. Vol. 44, pp. 2075–2092, 2015. 10.1002/eqe.2576
XXIV. Yang, J.; Yang, Y.; Deng, L.; Sun, B.; Gu, Z.; Zeng, L.; Zhao, S., : ‘Seismic Behaviors of Prefabricated Reinforced Concrete Shear Walls Assembled with a Cast-in-Place Vertical Joint’. Buildings. Vol. 13, 2023. 10.3390/buildings13123013

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Abstract:

The detailed examination of utilizing renewable energy sources, particularly integrating Photovoltaic (PV) arrays and Multilevel Inverters (MLI), is thorough and underscores the importance of addressing environmental issues linked to fossil fuels. The selection of Sinusoidal Pulse Width Modulation (SPWM) and its benefits, such as low switching losses and high efficiency, are well-articulated. The simulation results showing sinusoidal waveforms for resistive loads and the focus on reducing Total Harmonic Distortion (THD) using an LC filter further highlight the commitment to achieving high-quality power output. THD reduction is crucial for maintaining the stability and reliability of power systems. The incorporation of a seven-level MLI adds complexity and sophistication to the system, potentially allowing for more precise control over the output waveform and enhancing the overall performance of the renewable energy system. The consideration of factors like efficiency, reliability, and grid compatibility aligns with best practices in the design and implementation of renewable energy systems. Your approach clearly aligns with the broader industry trend towards cleaner and more sustainable energy solutions. Overall, the strategic and effective use of renewable energy, SPWM for control, addressing THD through an LC filter, and incorporating an eleven-level MLI showcases multi-order harmonic elimination for maximum power generation as presented in this paper.

Keywords:

Multilevel inverter (MLI),photovoltaic (PV),total harmonic distortion (THD),solar,sinusoidal pulse width modulation (SPWM),

Refference:

I. Alonso, O., Sanchis, P., Gubia, E., & Marroyo, L. “Cascaded H-bridge multilevel converter for grid-connected photovoltaic generators with independent maximum power point tracking of each solar array.” In Proceedings of the 34th IEEE Power Electronics Specialists Conference, Acapulco, Mexico, 15–19 June 2003, vol. 2, pp.731–735. New York: IEEE.
II. Barick, C. K., Mohapatra, B. K., Kabat, S. R., Jena, K., Ganthia, B. P., & Panigrahi, C. K. (2022, October). Review on Scenario of Wind Power Generation and Control. In 2022 1st IEEE International Conference on Industrial Electronics: Developments & Applications (ICIDeA) (pp. 12-17). IEEE.
III. Cecati, C., Dell’Aquila, A., Liserre, M., & Monopoli, V. G. “A passivity-based multilevel active rectifier with adaptive compensation for traction applications.” IEEE Transactions on Industry Applications, vol. 39, no. 5, pp. 1404–1413, 2003.
IV. Franquelo, L. G., Rodriguez, J., Leon, J. I., Kouko, S., & Portillo, R. “The age of multilevel converters arrives.” IEEE Industrial Electronics Magazine, vol. 2, no. 2, pp. 28–39, 2008.
V. Fu, Y., Kumar, J., Ganthia, B. P., & Neware, R. (2022). Nonlinear dynamic measurement method of software reliability based on data mining. International Journal of System Assurance Engineering and Management, 13(Suppl 1), 273-280.
VI. Ganthia, Bibhu Prasad, S. Barik, and Byamakesh Nayak. “Application of hybrid facts devices in DFIG based wind energy system for LVRT capability enhancements.” J. Mech. Cont. Math. Sci 15.6 (2020): 245-256.
VII. Ganthia, Bibhu Prasad, Subrat Kumar Barik, and Byamakesh Nayak. “Transient analysis of grid integrated stator voltage oriented controlled type-III DFIGdriven wind turbine energy system.” Journal of Mechanics of Continua and Mathematical Sciences 15.6 (2020): 139-157.
VIII. Ganthia, B. P., & Upadhyaya, M. “Bridgeless AC/DC Converter & DC-DC Based Power Factor Correction with Reduced Total Harmonic Distortion.” Design Engineering, pp. 2012-2018, 2021.
IX. Ganthia, B. P., Pradhan, R., Das, S., & Ganthia, S. “Analytical study of MPPT based PV system using fuzzy logic controller.” In 2017 International Conference on Energy, Communication, Data Analytics and Soft Computing (ICECDS), pp. 3266-3269, IEEE, 2017.
X. Ganthia, Bibhu Prasad, and B. M. Praveen. “Review on Scenario of Wind Power Generations in India.” Electrical Engineering 13, no. 2 (2023): 1-27p.
XI. Ganthia, Bibhu Prasad, and B. M. Praveen. “Design and Harmonic Elimination of sinusoidal pulse width modulation (SPWM) Based Five Level Cascaded H-Bridge Multilevel Inverter for Photovoltaic System for Educational Purposes.” Indonesian Journal of Teaching in Science 3, no. 2: 143-160.
XII. Ganthia, B. P., Sahu, P. K., & Mohanty, A. “Minimization Of Total Harmonic Distortion Using Pulse Width Modulation Technique.” IOSR Journal of Electrical and Electronics Engineering (IOSR-JEEE) e-ISSN, 2278-1676.
XIII. Ganthia, B. P., Monalisa Mohanty, Sushree Shataroopa Mohapatra, Rosalin Pradhan, Subhasmita Satapathy, Shilpa Patra, & Sunita Pahadasingh. “Artificial Neural Network Optimized Load Forecasting of Smartgrid using MATLAB.” Control Systems and Optimization Letters [Online], vol. 1, no. 1, pp. 46-51, 2023.
XIV. Gonzalez, R., Gubia, E., Lopez, J., & Marroyo, L. “Transformerless single-phase multilevel-based photovoltaic inverter.” IEEE Transactions on Industrial Electronics, vol. 55, no. 7, pp. 2694–2702, 2008.
XV. Hasan, M., Mekhilef, S., & Metselaar, I. H. “Photovoltaic System Modeling with Fuzzy Logic Based Maximum Power Point Tracking Algorithm.” International Journal of Photoenergy, vol. 2013, Article ID 762946, 10 pages, 2013. https://doi.org/10.1155/2013/762946.
XVI. Jena, S., Mishra, S., Ganthia, B. P., & Samal, S. K. (2022). Load Frequency Control of a Four-Area Interconnected Power System Using JAYA Tuned PID Controller and Derivative Filter. In Sustainable Energy and Technological Advancements: Proceedings of ISSETA 2021 (pp. 497-511). Singapore: Springer Singapore.
XVII. Kabat, Subash Ranjan, Chinmoy Kumar Panigrahi, and Bibhu Prasad Ganthia. “Fuzzy logic based fault current prediction in double fed induction generator based wind turbine system.” Materials Today: Proceedings 80 (2023): 2530-2538.
XVIII. Kabat, S. R., Panigrahi, C. K., & Ganthia, B. P. (2022). Comparative analysis of fuzzy logic and synchronous reference frame controlled LVRT capability enhancement in wind energy system using DVR and STATCOM. In Sustainable Energy and Technological Advancements: Proceedings of ISSETA 2021 (pp. 423-433). Singapore: Springer Singapore.

XIX. Khan, R. A., Farooqui, S. A., Sarwar, M. I., Ahmad, S., Tariq, M., Sarwar, A., Zaid, M., Ahmad, S., & Shah, N. M. A. “Archimedes Optimization Algorithm Based Selective Harmonic Elimination in a Cascaded H-Bridge Multilevel Inverter.” Sustainability, vol. 14, no. 1, p. 310, 2022. https://doi.org/10.3390/su14010310.
XX. Kjaer, S. B., Pedersen, J. K., & Blaabjerg, F. “A review of single-phase grid-connected inverters for photovoltaic modules.” IEEE Transactions on Industry Applications, vol. 41, no. 5, pp. 1292–1306, 2005.
XXI. Krithiga, G., & Mohan, V. “Elimination of Harmonics in Multilevel Inverter Using Multi-Group Marine Predator Algorithm-Based Enhanced RNN.” International Transactions on Electrical Energy Systems, vol. 2022, Article ID 8004425, 13 pages, 2022. https://doi.org/10.1155/2022/8004425.
XXII. Lai, J-S., & Peng, F. Z. “Multilevel converters—A new breed of power converters.” IEEE Transactions on Industry Applications, vol. 32, no. 3, pp. 509–517, 1996.
XXIII. Mannam, P., Manchireddy, S., & Ganthia, B. P. “Grid Tied PV with Reduced THD Using NN and PWM Techniques.” Design Engineering, pp. 2019-2027, 2021.
XXIV. Mohanty, R., Chatterjee, D., Mohanty, S., Dhanamjayulu, C., & Khan, B. “THD Reduction of Improved Single Source MLI Using Upgraded Black Widow Optimization Algorithm.” International Transactions on Electrical Energy Systems, vol. 2023, Article ID 6724716, 16 pages, 2023. https://doi.org/10.1155/2023/6724716.
XXV. Mohanty, M., Nayak, N., Ganthia, B. P., & Behera, M. K. (2023, June). Power Smoothening of Photovoltaic System using Dynamic PSO with ESC under Partial Shading Condition. In 2023 International Conference in Advances in Power, Signal, and Information Technology (APSIT) (pp. 675-680). IEEE.
XXVI. Ozdemir, E., Ozdemir, S., & Tolbert, L. M. “Fundamental-frequency-modulated six-level diode-clamped multilevel inverter for three-phase stand-alone photovoltaic system.” IEEE Transactions on Industrial Electronics, vol. 56, no. 11, pp. 4407–4415, 2009.
XXVII. Pahadasingh, S., Jena, C., Panigrahi, C. K., & Ganthia, B. P. (2022). JAYA Algorithm-Optimized Load Frequency Control of a Four-Area Interconnected Power System Tuning Using PID Controller. Engineering, Technology & Applied Science Research, 12(3), 8646-8651.
XXVIII. Refaai, M. R. A., Dhanesh, L., Ganthia, B. P., Mohanty, M., Subbiah, R., & Anbese, E. M. “Design and Implementation of a Floating PV Model to Analyse the Power Generation.” International Journal of Photoenergy, vol. 2022, Article ID 8004425, 2022.
XXIX. Riad, N., Anis, W., Elkassas, A., & Hassan, A. E. W. “Three-Phase Multilevel Inverter Using Selective Harmonic Elimination with Marine Predator Algorithm.” Electronics, vol. 10, no. 4, p. 374, 2021. https://doi.org/10.3390/electronics10040374.
XXX. Rodriguez, J. R., Dixon, J. W., Espinoza, J. R., Pontt, J., & Lezana, P. “PWM regenerative rectifiers: State of the art.” IEEE Transactions on Industrial Electronics, vol. 52, no. 1, pp. 5–22, 2005.
XXXI. Rodriguez, J. R., Lai, J-S., & Peng, F. Z. “Multilevel inverters: A survey of topologies, control, and applications.” IEEE Transactions on Industrial Electronics, vol. 49, no. 4, pp. 724–738, 2002.
XXXII. Rubavathy, S. J., Venkatasubramanian, R., Kumar, M. M., Ganthia, B. P., Kumar, J. S., Hemachandu, P., & Ramkumar, M. S. “Smart Grid Based Multiagent System in Transmission Sector.” In 2021 Third International Conference on Inventive Research in Computing Applications (ICIRCA), pp. 1-5, IEEE, 2021.
XXXIII. Sahu, P. K., Mohanty, A., Ganthia, B. P., & Panda, A. K. “A multiphase interleaved boost converter for grid-connected PV system.” In 2016 International Conference on Microelectronics, Computing and Communications (MicroCom), pp. 1-6, IEEE, 2016.
XXXIV. Thenmalar, K., Kiruba, K., Raj, P., & Ganthia, B. P. “A Real Time Implementation of ANN Controller to Track Maximum Power Point in Solar Photovoltaic System.” Annals of the Romanian Society for Cell Biology, vol. 25, no. 6, pp. 10592-10607, 2021.
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XXXVI. Udayakumar, C., Kumarasamy, S., Samikannu, R., Rajamani, M. P. E., Krishnamoorthy, V., & Murugesan, S. “Tournament Selected Glowworm Swarm Optimization Based Measurement of Selective Harmonic Elimination in Multilevel Inverter for Enhancing Output Voltage and Current.” Mathematical Problems in Engineering, vol. 2022, Article ID 5845249, 11 pages, 2022. https://doi.org/10.1155/2022/5845249.
XXXVII. Vadivel Kannan, L., Ganthia, B. P., & N. C. R. “Cascade H Bridge Multilevel Inverter with PWM for Lower THD, EMI & RFI Reduction.” Annals of the Romanian Society for Cell Biology, vol. 25, no. 6, pp. 2972–2977, 2021. https://www.annalsofrscb.ro/index.php/journal/article/view/6013.

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Abstract:

In this paper, the framework of Data Hiding on Digital Images Using Deep Neural Network (DNN). Here DeepSteg architecture is considered to evaluate the performance of the multiple secret images that can be concatenated to the single cover image, the image data will be hidden on the single cover image using the Tiny ImageNet dataset. The proposed model outperformed earlier results. To compare our results two parameters, normally Secret loss(λ_s) and cover loss(λ_c) are considered. Our plan is to use deep neural networks for the encoding and decoding of multiple secret images inside a single cover image of a similar goal.

Keywords:

Deep Neural network,Deep Steganography,Multiple Secret Images,Single Cover Image,Tiny ImageNet dataset,

Refference:

I. Baluja, S. Hiding images in plain sight: Deep steganography. In Guyon, I., Luxburg, U. V., Bengio, S., Wallach, H., Fergus, R., Vishwanathan, S., and Garnett, R. (eds.), Advances in Neural Information Processing Systems 30, pp. 2069–2079. Curran Associates, Inc., 2017.

II. Bikash Chandra Bag, Hirak Kumar Maity , Chaitali Koley. : ‘UNET MOBILENETV2: MEDICAL IMAGE SEGMENTATION USING DEEP NEURAL NETWORK (DNN)’. J. Mech. Cont. & Math. Sci., Vol.-18(1), pp 21-29, 2023. 10.26782/jmcms.2023.01.00002

III. Deng, J., Dong, W., Socher, R., Li, L.-J., Li, K., and Fei-Fei, L. ImageNet: A Large-Scale Hierarchical Image Database. In CVPR09, 2009.

IV. Hayes, J. and Danezis, G. Generating steganographic images via adversarial training. In NIPS, 2017.

V. Ingham, F. Deepsteg: Implementation of hidding images in plain sight: Deep steganography in pytorch.

VI. Kreuk, F., Adi, Y., Raj, B., Singh, R., and Keshet, J. Hide and speak: Deep neural networks for speech steganography, 2019.

VII. Muzio, A. Deep-steg: Implementation of hidding images in plain sight: Deep steganography in keras.

VIII. Zhu, J., Kaplan, R., Johnson, J., and Fei-Fei, L. Hidden: Hiding data with deep networks. CoRR, abs/1807.09937, 2018.

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Abstract:

The VANET customized vehicle network's versatility, cost-effectiveness, accurate sensing, and potential to open up new and exciting remote sensing applications make it an intriguing subject of study. VANET, short for Vehicular Ad Hoc Network, is a network designed to build an automobile network for a specific purpose. VANETs are being developed as reliable networks used by automobiles to prevent road accidents and ensure passenger safety. They also allow automobiles to communicate, sending emergency alerts and entertainment updates on highways and in cities. VANET is a mobile network that predicts and assists drivers and others in life-threatening and road safety-related circumstances. Despite their many benefits, these networks face many challenges due to their nature. Random movement patterns and high-speed mobility change network structure, resulting in frequent deliveries. This issue is especially important in dedicated vehicle networks, which we will discuss here. This article investigates the possibility of transitioning from VANET to the incorporation of LTE, SDN, and ultimately 5G to establish performance.

Keywords:

Automobile network,Remote Sensing Applications,Road Accidents Vehicular Ad Hoc Network,

Refference:

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XIV. F. Aadil, S. Rizwan and A. Akram, “Vehicular Ad Hoc Networks (VANETs), Past Present and Future: A survey,” In HET-NETs, The Seventh International Working, England, UK, 2013.
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Abstract:

Extension of some Integral Transform by the Method of Multiple Integrals by Lebesgue measurable and Lebesgue integrable.

Keywords:

Fourier transform,Inverse Fourier transform,Lebesgue measurable,

Refference:

I. AL-Qmari S. K. Q. (2020), Estimation of a modified integral associated with a special function kernel of fox’s h-function type, Commun. Korean Math. Soc. , No. 1, pp. 125–136.
II. Bhatter Sanjay (2022), On Certain New Results of Fractional Calculus InvolvingProduct of Generalized Special Functions , Int. J. Appl. Comput. Math. doi.org/10.1007/s40819-022-01253-0.
III. Choi J. H.(2013) ,Applications of multivalent functions associated with generalized fractional integral operator, Scientific Research, Advances in Pure Mathematics,3,1- 5.
IV. Debnath, L., Bhatta, D.: Integral Transforms and Their Applications, 3rd edn. Chapman Haubold H. J.(2009) , Mittag-Leffler Functions and their applications, Journal of Applied Mathematics, arXiv:0909.0230v2.
V. Gupta K.(2011), A Study of modified H-transform and generalized fractional integral operator of weyl type, International Journal of Pure and Applied Sciences and Technology, 7(1) (2011), pp. 59-67, ISSN 2229-6107.
VI. Gupta K. and Vandana Agrawal (2010) ,A Theorem Connecting the H-Transform and Fractional Integral Operators Involving the Multivariable H-Function, Tamsui Oxford Journal of Mathematical Sciences, Aletheia University, 26(4) , 383-395.
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X. Tassaddiq Asifa (2022), Unified Approach to Fractional Calculus Images Involving the Pathway Transform of Extended k-Gamma Function and Applications, Adv. Of Mathematical Physics, Vol. (22)| ArticleID 9698299, https://doi.org/10.1155/2022/9698299.
XI. Watugala G. K.(1998), Sumudu transform- a new integral transform to solve differential equations and control engineering problems. Math. Engr. Indust., 6(4): 319-329.

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Abstract:

In this paper, we give new four notions of fuzzy soft α -T_1 topological space using the fuzzy soft points concept. We have discussed some implications and theorems, along with their proofs. Moreover, we have presented the hereditary, productive, and projective properties with proof. Finally, we have shown that our given notions are preserved under bijective, fuzzy soft open, and continuous mappings.

Keywords:

Soft set,Fuzzy soft set,Fuzzy soft topological space,Quasi-coincidence,Fuzzy Soft T₁ topological spaces,

Refference:

I. Ahmad B., Kharal A. : On Fuzzy Soft Sets, Hindawi Publishing Corporation, Advances in Fuzzy Systems Article ID 586507, 2009.
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III. Hannan Miah and Ruhul Amin : Some Features of Pairwise α-T_0 Spaces in Supra Fuzzy Bitopology, Journal of Mechanics of Continua and Mathematical Sciences, 15(11), pp. 1-11, 2020.
IV. Kandil A., Tantawy O. A. E., El-Sheikh S. A. and Abd El-latif A. M. : Some fuzzy soft topological properties based on fuzzy semi open soft sets, South Asian J. Math., 4 (4), pp. 154–169, 2014.
V. Kharal A. and Ahmad B.: Mappings on fuzzy soft classes, Hindawi Publishing Corporation, Adv. Fuzzy Syst., 2009.
VI. Mishra S. and Srivastava R. : On T_0 and T_1 Fuzzy Soft Topological Spaces, Ann. Fuzzy Math. Inform., 10 (4), pp. 591-605, 2015.
VII. Molodtsov D. : Soft Set Theory First Results, Comput. Math. Appl., 37 (4-5), pp 19-31, 1999.
VIII. Nazmul S. and Samanta S. K. : Soft Topological Groups, Kochi J. Math., 5, pp. 151-161, 2010.
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X. Roy S. and Samanta T. K. : A Note on Fuzzy Soft Topological Spaces, Ann. Fuzzy Math. Inform., 5 (2), pp. 305-311, 2012.
XI. Ruhul Amin and Raihanul Islam : New Concepts on R_1 Fuzzy Soft Topological Spaces, Ann. Fuzzy Math., 22 (2), (October), pp. 123-132, 2021.
XII. Ruhul Amin, Raihanul Islam, Sudipto Kumar Shaha and Saikh Shahjahan Miah : Some properties of T_0 fuzzy soft topological spaces in quasi-coincidence sense, Journal of Mechanics of Continua and Mathematical Sciences, 17(4), pp. 8-20, 2022.
XIII. Shabir M. and Naz M. : On Soft Topological Spaces, Comput. Math. Appl., 61, pp. 1786-1799, 2011.
XIV. Saleh S., Abd El-Latif A. M. and Al-Salemi A. : On Separation Axioms in Fuzzy Soft Topological Spaces, South Asian Journal of Mathematics, 8 (2), pp. 92-109, 2018.
XV. Tanay B. and Kandemir M. B. : Topological Structure of Fuzzy Soft Sets, Computer and Mathematics with Applications, 61, pp. 2952-2957, 2011.
XVI. Varol B. P. and Aygun H. : Fuzzy Soft Topology, Hacettepe Journal of Mathematics and Statistics, 41 (3), pp. 407-419, 2012.
XVII. Zadeh, L. A. : Fuzzy sets. Information and Control , 8, pp. 338-353, 1965.

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Abstract:

The fourth industrial revolution, in short Industry 4.0 is the next stage in the digitization of the industrial sector and is being driven by disruptive trends including the growth of data and connectivity, analytics, human-machine interaction, and advancements in robotics. For the past ten years, Industry 4.0 consistently addressed both the industry’s strengths and weaknesses. Industry 4.0 is limited by the higher productivity that smart manufacturing systems provide. The new version of Industry 4.0 is termed Industry 5.0 and it refers to the fifth industrial revolution and is an emerging concept that builds on the advancements of Industry 4.0. Thus, industry 5.0 is an extension and further advancement of Industry 4.0, which focuses on automation, connectivity, and data exchange in manufacturing processes. Industry 5.0 introduces a new level of human-machine collaboration and emphasizes the importance of human creativity and skills alongside advanced technologies. This study discusses the opportunities and directions of future mathematical research towards Industry 5.0.

Keywords:

Industry 4.0,Industry 5.0,Artificial Intelligence,Big Data,Cryptography,Machine Learning,Optimization Techniques,Quantum Computing,Robotics,

Refference:

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XLVIII. S. Tatiana, V. Natalia, G. Nadezhda. : Towards sustainability through Industry 4.0 and Society 5.0, International Review. Vol. (3-4): pp. 48-54, 2020. 10.5937/intrev2003048S.
XLIX. S. Yin, D. Pamucar, K. Ullah, H. Garg. : ‘Editorial: Fuzzy mathematical model and optimization in digital green innovation for Industry 5.0’. Frontiers of Environmental Science. 11:1269419, 2023. 10.3389/fenvs.2023.1269419.
L. T. Ahmed, C. L. Karmaker, S. B. Nasir, M. A. Moktadir, S. K. Paul. : ‘Modeling the artificial intelligence-based imperatives of industry 5.0 towards resilient supply chains: A post-COVID-19 pandemic perspective’. Computers & Industrial Engineering. Vol. 177:109055, 2023. 10.1016/j.cie.2023.109055.
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LIII. X. Li, X. Gao, S. A. Shaikh, M. Zeng, G. Huang, N. M. F. Qureshi, D. Qiao. : ‘NOMA-based cognitive radio network with hybrid FD/HD relay in industry 5.0’. Journal of King Saud University-Computer and Information Sciences. Vol. 35(6), 101363, 2023. 10.1016/j.jksuci.2022.08.013.
LIV. X. Xu, Y. Lu, B. Vogel-Heuser, L. Wang. : ‘Industry 4.0 and Industry 5.0-Inception, conception and perception’. Journal of Manufacturing System. Vol. 61, pp. 530-535, 2021. 10.1016/j.jmsy.2021.10.006.
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Abstract:

We explore machine learning strategies and evaluate their viability in distinguishing characteristics that separate secure websites from phishing ones. Given the essential need to defend delicate information and maintain network integrity, we aim to determine the most proficient strategy for identifying phishing websites. Our research focuses on the Random Forest Classifier, illustrating its predominance over other strategies. We have achieved significant improvements in detection rates, with the Random Forest Classifier accomplishing an F1 score of 0.99, precision of 0.99, recall of 0.99, and an AUC of 1.00, outperforming other classifiers. By specifying each strategy and utilizing various assessment methods for visual performance representation, we provide a robust model for phishing detection.

Keywords:

Phishing assault recognition,AI,Random Forest,phishing site location,

Refference:

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XII. H. Khan, S. Ahmad, N. Saleem, M. U. Hashmi, Q. Bashir, “Scheduling Based Dynamic Power Management Technique for offline Optimization of Energy in Multi Core Processors” Int. J. Sci. Eng. Res, Vol.9, No.12, pp 6-10, 2018
XIII. H. Khan, K. Janjua, A. Sikandar, M. W. Qazi, Z. Hameed, “An Efficient Scheduling based cloud computing technique using virtual Machine Resource Allocation for efficient resource utilization of Servers” In 2020 International Conference on Engineering and Emerging Technologies (ICEET), IEEE, pp 1-7, 2020
XIV. Hammad, M., Jillani, R. M., Ullah, S., Namoun, A., Tufail, A., Kim, K. H., & Shah, H, “Security framework for network-based manufacturing systems with personalized customization”, An industry 4.0 approach, Sensors, vol. 23. No. 17-55, 2022
XV. H. Khan, Q. Bashir, M. U. Hashmi, “Scheduling based energy optimization technique in multiprocessor embedded systems” In 2018 International Conference on Engineering and Emerging Technologies (ICEET), IEEE, pp 1-8, 2018
XVI. H. Khan, A. Yasmeen, S. Jan, U. Hashmi, “Enhanced Resource Leveling Indynamic Power Management Techniqueof Improvement In Performance For Multi-Core Processors”, Journal Of Mechanics Of Continua And Mathematical Sciences, Vol.6, No.14, pp. 956-972, 2019
XVII. H. Khan, K. Janjua, A. Sikandar, M. W. Qazi, Z. Hameed, “An Efficient Scheduling based cloud computing technique using virtual Machine Resource Allocation for efficient resource utilization of Servers” In 2020 International Conference on Engineering and Emerging Technologies (ICEET), IEEE, pp 1-7, 2020
XVIII. H. Huang, J. Tan And L. Liu, “Countermeasure Techniques For Deceptive Phishing Attack”, International Conference On New Trends In Information And Service Science, Beijing, pp. 636-641, 2009
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XX. H. Khan, M. U. Hashmi, Z. Khan, R. Ahmad, A. Saleem, “Performance Evaluation for Secure DES-Algorithm Based Authentication & Counter Measures for Internet Mobile Host Protocol” IJCSNS Int. J. Comput. Sci. Netw. Secur, Vol.18, No.12, pp 181-185, 2018
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XXII. M. Y. A. Khan, F. Khan, H. Khan, S. Ahmed, M. Ahmad, “Design and Analysis of Maximum Power Point Tracking (MPPT) Controller for PV System” Journal of Mechanics of Continua and Mathematical Sciences, Vol.14, No.1, pp 276-288, 2019
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XXIV. M. Y. A. Khan, “A high state of modular transistor on a 105 kW HVPS for X-rays tomography Applications”, Sukkur IBA Journal of Emerging Technologies, Vol.2, No.2, pp 1-6, 2019
XXV. M. Shah, S. Ahmed, K. Saeed, M. Junaid, H. Khan, “Penetration testing active reconnaissance phase–optimized port scanning with nmap tool” In 2019 2nd International Conference on Computing, Mathematics and Engineering Technologies (iCoMET), IEEE, pp 1-6, 2019
XXVI. M. Y. A. Khan, M. Ibrahim, M. Ali, H. Khan, E. Mustafa, “Cost Benefit Based Analytical Study of Automatic Meter Reading (AMR) and Blind Meter Reading (BMR) used by PESCO (WAPDA),” In 2020 3rd International Conference on Computing, Mathematics and Engineering Technologies (iCoMET), IEEE, pp 1-7, 2020
XXVII. M. Y. A. Khan, “Enhancing Energy Efficiency in Temperature Controlled Dynamic Scheduling Technique for Multi Processing System on Chip” Sukkur IBA Journal of Emerging Technologies, Vol.2, No.2, pp 46-53,2019
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XXXI. S. Khan, I. Ullah, M. U. Rahman, H. Khan, A. B. Shah, R. H. Althomali, M. M. Rahman, “Inorganic-polymer composite electrolytes: basics, fabrications, challenges and future perspectives” Reviews in Inorganic Chemistry, Vol.44, No.3, pp 1-29, 2024.
XXXII. S. Khan, I. Ullah, H. Khan, F. U. Rahman, M. U. Rahman, M. A. Saleem, A. Ullah, “Green synthesis of AgNPs from leaves extract of Salvia Sclarea their characterization, antibacterial activity and catalytic reduction ability” Zeitschrift für Physikalische Chemie, Vol.238, No.5, pp 931-947, 2024
XXXIII. T. M. Gondal, Z. Hameed, M. U. Shah, H. Khan, “Cavitation phenomenon and its effects in Francis turbines and amassed adeptness of hydel power plant” In 2019 2nd International Conference on Computing, Mathematics and Engineering Technologies (iCoMET), IEEE, pp 1-9, 2019

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Abstract:

This study investigates the Atangana-Baleanu time-stochastic fractional neutral integro-differential equation, a complex mathematical model with broad applications in various scientific disciplines. Utilizing Banach's fixed point theory, we rigorously establish the existence and uniqueness of the mild solution to this equation. Our analysis centrally revolves around investigating the Mittag-Leffler non-singular and non-local kernel, emphasizing its crucial significance in elucidating the behavior of the equation. By integrating concepts from fractional differential equations and stochastic differential systems, we contribute to a deeper comprehension of these mathematical phenomena. Our findings not only contribute significantly to advancing theoretical understanding but also establish a solid groundwork for practical applications across various fields.

Keywords:

Existence and uniqueness,Mittag-Leffler Non-singular and non-local kernel,Fractional differential equations,Stochastic differential system and fixed point theorem.,

Refference:

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II. Arqub, O.A.: ‘Numerical solutions of integrodifferential equations of Fredholm operator type in the sense of the Atangana-Baleanu fractional operator’, Chaos Solitons Fractals, Vol. 117 (2018), Pages 117-124.
III. Atangana, A., Baleanu, D.: ‘New fractional derivatives with non-local and nonsingular kernel, Theory and application to heat transfer model’, Thermal Sci., Vol. 20 (2016), Pages 763-769.
IV. Baleanu, D., Fernandez, A.: ‘On some new properties of fractional derivatives with Mittag-Leffler kernel’, Commun Nonlinear Sci Numer Simul., Vol. 59 (2018), Pages 444-462.
V. Bose, C.S., Udhayakumar, R., Elshenhab, A.M., Sathish Kumar, M., Ro, J.S.: ‘Discussion on the Approximate Controllability of Hilfer Fractional Neutral Integro-Differential Inclusions via Almost Sectorial Operators’, Fractal and Fractional, Vol. 6(10), Page 607.
VI. Caputo, M., Fabrizio, M.: ‘A new definition of fractional derivative without singular kernel’, Progr Fract Differ Appl., Vol. 1 (2015), Pages 73-85.
VII. Foondun, M., Liu, W., Tian, K.: ‘On some properties of a class of fractional stochastic heat equations’, J Theoret Probab., Vol. 30 (2017), Pages 1310-1333.
VIII. Guendouzi, T., Hamada, I.: ‘Existence and controllability result for fractional neutral stochastic integro-differential equations with infinite delay’, Advanced Modeling and Optimization, Vol. 15(2) (2013), Pages 281-299.
IX. Kilbas, A., Srivastava, H., Trujillo, J.J.: ‘Theory and Applications of Fractional Differential Equations’, Elsevier, Amsterdam (2006).
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XII. Nane, E., Nwaeze, E.R., Omaba, M.E.: ‘Asymptotic behavior and non-existence of global solution to a class of conformable time-fractional stochastic differential equation’, Statist Probab Lett., Vol. 163 (2020), Page 108792.
XIII. Omaba, M.E., Enyi, C.D.: ‘Atangana-Baleanu time-fractional stochastic integrodifferential equation’, Partial Differential Equations in Applied Mathematics, Vol. 4 (2021), Page 100100.
XIV. Omaba, M.E.: ‘Growth moment, stability and asymptotic behaviours of solution to a class of time fractal fractional stochastic differential equation’, Chaos Solitons Fractals, Vol. 147 (2021), Page 110958.
XV. Omaba, M.E.: ‘On space-fractional heat equation with non-homogeneous fractional time Poisson process’, Progr Fract Differ Appl., Vol. 6(1) (2020), Pages 67-79.
XVI. Podlubny, I.: ‘Fractional Differential Equations’, Academic Press, New York (1999).

XVII. Ravichandran, C., Logeswari, K., Jarad, F.: ‘New results on existence in the framework of Atangana-Baleanu derivative for fractional integro-differential equations’, Chaos Solitons Fractals, Vol. 125 (2019), Pages 194-200.
XVIII. Sakthivel, R., Ganesh, R., Suganya, S.: ‘Approximate controllability of fractional neutral stochastic system with infinite delay’, Reports on Mathematical Physics, Vol. 70(3) (2012), Pages 291-311.
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XXI. Sathish Kumar, M., Bazighifan, O., Al-Shaqsi, F., Wannalookkhee, K., Nonlaopon: ‘Symmetry and its role in oscillation of solutions of third-order differential equations’, Symmetry, Vol. 13, No. 8, ID 1485.
XXII. Sathish Kumar, M., Deepa, M., Kavitha, J., Sadhasivam, V.: ‘Existence theory of fractional order three-dimensional differential system at resonance’, Mathematical Modelling and Control, Vol. 3(2) (2023), Pages 127-138.
XXIII. Sathish Kumar, M., Ganesan, V.: ‘Asymptotic behavior of solutions of third-order neutral differential equations with discrete and distributed delay’, AIMS Mathematics, Vol. 5, No. 4 (2020), Pages 3851-3874;
XXIV. Sathish Kumar, M., Veeramalai, G., Janaki, S., Ganesan, V.: ‘Qualitative behavior of third-order damped nonlinear differential equations with several delays’, Journal of Mechanics of Continua and Mathematical Sciences, Vol. 19(4) (2024), Pages 60-82.
XXV. Sharma, M., Dubey, S.: ‘Controllability of nonlocal fractional functional differential equations of neutral type in a Banach space’, International Journal of Dynamical Systems and Differential Equations, 5, 2015, 302-321
XXVI. Vijaykumar, V., Ravichandran, C., Murugesu, R., Trujillo, J.J.: ‘Controllability results for a class of fractional semilinear integro-differential inclusions via resolvent operators’, Applied Mathematics and Computation, Vol. 247 (2014), Pages 152-161.
XXVII. Zhou, Y.: ‘Basic Theory of Fractional Differential Equations’, World Scientific, Singapore (2014).

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Abstract:

Because of its high transmission information rates, accessibility of permit to drive range, signal security, and cost proficiency, free space optical (FSO) correspondence is turning out to be progressively appealing as an option for radio recurrence (RF) correspondence. A 32-channel DWDM FSO framework with an information throughput of 1.28 Tbps has been planned in this review. The recommended framework was tried over a scope of distances (5-20 km) and for three distinct sorts of downpour (light, medium, and weighty), with constriction upsides of (1.988, 5.844, and 9.29) dB, individually. The exhibition of elective balance organizations like NRZ and RZ, as well as 5 situations of fluctuating information force of (- 5,- 10,0,5,10) dBm, has been examined in this paper. The framework execution worked on as the information power was expanded, as per the outcomes from the broken down boundaries of QF and BER. Furthermore, it has been found that utilizing RZ creates improved results for light downpour cases in totally input power situations. While the RZ regulation sort performed better in medium downpours for distances up to 5 km, the NRZ adjustment style is suggested for longer distances. Furthermore, in a weighty downpour climate, using 0 dBm and 5 dBm power showed that NRZ is extensively prevalent, while expanding the capacity to 10 dBm furnished substantially more versatile results regarding the got distance of just 5 km.

Keywords:

Downpour,Fluctuating Information Force,Free Space Optical,Radio Recurrence,

Refference:

I. Abdulwahid, M. M., & KURNAZ, S. (2023). Implementation of 2D Ray SBR Modeling for different MIMO Antenna Array placement in Outdoor communication using Wireless InSite software.
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III. Abdulwahid, M. M., Kurnaz, S., Türkben, A. K., Hayal, M. R., Elsayed, E. E., & Juraev, D. A. (2024). Inter-satellite optical wireless communication (Is-OWC) trends: a review, challenges and opportunities. Engineering Applications, 3(1), 1-15.
IV. Abdulwahid, M. M., & Kurnaz, S. (2023, July). Implementation of two polarization DQPSK WDM Is-OWC system with different precoding schemes for long-reach GEO Inter Satellite Link. In International Conference on Green Energy, Computing and Intelligent Technology (GEn-CITy 2023) (Vol. 2023, pp. 134-141). IET.
V. Almetwali, A. S., Bayat, O., Abdulwahid, M. M., & Mohamadwasel, N. B. (2022, November). Design and analysis of 50 channel by 40 Gbps DWDM-RoF system for 5G communication based on fronthaul scenario. In Proceedings of Third Doctoral Symposium on Computational Intelligence: DoSCI 2022 (pp. 109-122). Singapore: Springer Nature Singapore.
VI. A. B. Mohammad, “Optimization of FSO System in Tropical Weather Using Multiple Beams”, In: Proc. of International Conf. on IEEE Photonics (ICP), pp. 109-112, 2014.
VII. A. Ahmed, A. Singh, A. Singh, and S. Kaur, “Performance Analysis of WDM-MIMO Free Space Optical System Under Atmospheric Turbulence”, In: Proc. of International Conf. on Signal Processing and Integrated Networks (SPIN), pp. 820-825, 2019.
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XIX. Mohsen, D. E., Abbas, E. M., & Abdulwahid, M. M. (2022, June). Design and Implementation of DWDM-FSO system for Tbps data rates with different atmospheric Attenuation. In 2022 International Congress on Human-Computer Interaction, Optimization and Robotic Applications (HORA) (pp. 1-7). IEEE.
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XXVIII. Sharma, A., Kaur, S., & Chaudhary, S. (2021). Performance analysis of 320 Gbps DWDM—FSO System under the effect of different atmospheric conditions. Optical and Quantum Electronics, 53(5), 1-9.‏‏
XXIX. S. Kaur and A. Kakati, “Analysis of Free Space Optics Link Performance Considering the Effect of Different Weather Conditions and Modulation Formats for Terrestrial Communication”, Journal of Optical Communication, 2018
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XXXI. S. Retal and A. Idrissi, “A multi-objective optimization system for mobile gateways selection in vehicular Ad-Hoc networks,” Comput. Electr. Eng., vol. 73, pp. 289–303, 2019.
XXXII. S. Roshani et al., “Design of a compact quad-channel microstrip diplexer for L and S band applications,” Micromachines (Basel), vol. 14, no. 3, 2023.
XXXIII. S. I. Yahya et al., “A New Design method for class-E power amplifiers using artificial intelligence modeling for wireless power transfer applications,” Electronics (Basel), vol. 11, no. 21, p. 3608, 2022.
XXXIV. S. A. Abdulameer et al., “Cyber Security Readiness in Iraq: Role of the Human Rights Activists,” International Journal of Cyber Criminology, vol. 16, pp. 1–14, 2022.
XXXV. S. Kaur, “Analysis of Inter-Satellite Free-Space Optical Link Performance Considering Different System Parameters”, Opto-Electronics Review, Vol. 27, No. 1, pp. 10- 13, 2019.
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XXXVII. S. Parkash, A. Sharma, H. Singh, and H. P. Singh, “Performance investigation of 40 GB/s DWDM over free space optical communication system using RZ modulation format,” Adv. Opt. Technol., vol. 2016, 2016.
XXXVIII. Y. S. Mezaal and S. F. Abdulkareem, “New microstrip antenna based on quasi-fractal geometry for recent wireless systems,” in 2018 26th Signal Processing and Communications Applications Conference (SIU), 2018.
XXXIX. Y. S. Mezaal, L. N. Yousif, Z. J. Abdulkareem, H. A. Hussein, and S. K. Khaleel, “Review about effects of IOT and Nano-technology techniques in the development of IONT in wireless systems (2018),” International Journal of Engineering and Technology, vol. 7, no. 4, 2018.
XL. Y. S. Mezaal, H. H. Saleh, and H. Al-saedi, “New compact microstrip filters based on quasi fractal resonator,” Adv. Electromagn., vol. 7, no. 4, pp. 93–102, 2018.
XLI. Z. Mahlobogwane, P. A. Owolawi, and O. Sokoya, “Multiple Wavelength Propagation in Free Space Optical Wireless Channel”, In: Proc. of International Conf. on Advances in Big Data Computing and Data Communication Systems (icABCD), pp. 1-6, 2018.

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Abstract:

In this paper, we establish several interesting mutual relationships between two integral transforms of convolutions transform have been established

Keywords:

Convolution Theorem,Inverse Laplace Transform,Laplace Transform,

Refference:

I. Bhartiya, P.L.(1965), Mutual relations between different convolution transform of a function, Jl. Of math, Jabalpur Univ. P.47-54.
II. Chang, K. S., Kim, B. S. and Yoo, I. (2000), Integral transform and convolution of analytic functionals on abstract Wiener space Number. Funct. Anal.Optim. , 21: 97 – 105.
III. Erdilyi, A. (1954), Higher transcendental function Vol.1, Mcgrow Hill Book Co., New York.
IV. Hirschman, I. I. & Widder D. V. (1955),The convolution transform, Princeton University Press.
V. Huffman, T., Park, C. and Skoug, D. (1996), Convolution and Fourier–Feynman transforms of functionals involving multiple integrals. Michigan Math. J,43: 247 – 261.
VI. Huffman, T., Park, C. and Skoug, D. (1997), Convolution and Fourier–Feynman transforms. Rocky Mt. J. Math. , 27: 827 – 841.
VII. Kim, B. J., Kim, B. S. and Skoug, D. (2004) Integral transforms, convolution products and first variations. Int. J. Math. Math. Soc.,11: 579 – 598.
VIII. Kim, J. G., KO, J. W., Park, C. and Skoug, D. (1999) Relationships among transforms, convolutions and first variations. Int. J. Math. Math. Sci., 22. pp. 191 – 204.
IX. N.M. Tuan, P.D. Tuan, Generalized convolutions relative to the Hartley transforms with applications, Sci. Math. Jpn. 70 (2009), 77–89.
X. Park, C., Skoug, D. and Storvick, D. (1998)Relationships among the first variation, the convolution product and the Fourier–Feynman transform Rocky Mt. J. Math. , 28: 1447 – 1468.
XI. Sharma, H. N. (1973), Evaluation of definite integrals by the method of convolution transform Indian Jl. Of math, Vol.15, No.1.
XII. Singh, B.P. (1989), Ph.D. thesis, Integral transform with special reference to convolution transform, Ranchi University.

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Abstract:

Important areas for study in the field of act theory include expansions for the notion for extending acts. There has already been an introduction to the idea of extending acts. Our focus recently has been on semi-extending acts as a means for investigating one of these generalizations. The condition that every sub-act for an S-act  has been semi -large in a retracted from has been what defines it as a semi-extending S-act. Based on this, we provide several characteristics for semi-extending acts. Also included are examples that show how this idea works. We prove relationships between semi-extending acts and related conceptions utilizing a fully essential notion.

Keywords:

Semi ⋂-large sub-acts,⋂-large sub-acts,strongly closed sub-acts,Closed sub-acts,fully ⋂-large acts,

Refference:

I. J. Ahsan and L.Zhongkui, prime and semiprime acts over monoids with zero, Math.J., Ibaraki University, Vol.33, pp. 9 – 15, 2001. https://www.researchgate.net/publication/251080153_Prime_and_semiprime_acts_over_monoids_with_zero
II. Z. A. AL-Bast and P. F. Smith, Multiplication modules, Communication in Algebra, Vol. 10, 755-779, 2007. https://www.tandfonline.com/doi/pdf/10.1080/00927878808823601
III. P. Berthiaume, The injective envelope for S-sets, Canad . Math. Bull.,10, 261 – 273, 2018. https://www.cambridge.org/core/journals/canadian-mathematical-bulletin/article/injective-envelope-of-ssets/CC5C688B45202403E48AE8B5C75CEC0F
IV. N. V. Dungh, D. V. Huynh, P. F. Smith and R. Wisbauer, Extending modules, Pitman Researh Notes in Mathematics Series 313, Longmon, New York, 2019. https://www.researchgate.net/publication/330967788_Extending_modules
V. E. H., Feller and R. L.Gantos, Indecomposable and injective S-acts with zero , Math.Nachr., 41, pp37-48,1969. https://doi.org/10.1002/mana.19690410104
VI. C. V. Hinkle and Jr., The extended centralizer of an S-set, Pacific journal for mathematics, Vol.53, No.1, pp163-170, 1974. https://msp.org/pjm/1974/53-1/pjm-v53-n1-p14-s.pdf
VII. M. Kilp, U. Knauer and A.V. Mikhalev, Monoids acts and categories. Walter de Gruyter, Berlin, New York, 2000. https://doi.org/10.1515/9783110812909
VIII. A. M. Lopez, Jr. and J. K. Luedeman, Quasi-injective S-acts and their S-endomorphism Semigroup, Czechoslovak Math.J., Vol. 29, No.104, pp 97-104,1979. https://eudml.org/doc/13107
IX. A. M. Lopez, Jr. and J.K.Luedeman , The Bicommutator for the injective hull for a non- singular semigroup , Semigroup forum , Vol.12 , pp71-77, 1976. https://link.springer.com/article/10.1007/BF02195910
X. R. Mohammad and E.Majid, Strongly duo and duo right S-acts , Italian journal for pure and applied mathematics,32, 143-154, 2014. https://ijpam.uniud.it/online_issue/201432/14-RooeintanErshad.pdf
XI. A. Shaymaa , Generalizations of injective S-acts, Communications in algebra, Vol.51,No.4 , PP.1743-1751, 2022. https://doi.org/10.1080/00927872.2022.2141766
XII. A. Shaymaa and A. A. Ahmed, ⋂-large pseudo injective acts, Journal for discrete mathematical sciences and cryptography, Vol.25, No.2, PP.511-522, 2022. DOI:10.1080/09720529.2020.1734294
XIII. A. Shaymaa, Extending and P-extending S-act over monoids , International Journal for advanced scientific and technical research, Vol.2 , No. 7, pp.171-178,2017. https://rspublication.com/ijst/2017/april17/19.pdf
XIV. K. Sungjin and K.Jupil , Weakly large subsystems of S-system , J. for Chungcheong Math. Soc., Vol.20, no.4, pp486-493,2007. http://www.ccms.or.kr/data/pdfpaper/jcms20_4/20_4_485.pdf
XV. T. Yan , A.Javed , X.FEI and G.XIAO, Monoids characterized by their injectivity and projectivity classes, Advances in mathematics, Vol.36,No.3 ,pp. 321-326,2007. http://china.oriprobe.com/articles/12275678/Monoids_Characterized_by_Their_Injectivity_and_Pro.htm

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Abstract:

Cloud computing plays a vital role, which is used to access computing resources and information online. There are a lot of challenges in accessing cloud computing systems. One of the major challenges among these is resource Management which includes scheduling, allocation, and sharing. In this paper, the Hybrid Genetic Modified Whale optimization algorithm which is a combined Genetic and Modified Whale optimization algorithm to analyze the performance of the cloud computing system such as task completion time, execution cost, speedup, and efficiency with proper allocation and sharing of resources The performance of the proposed algorithm is compared with Genetic algorithm and Whale optimization algorithm. The main target of this Proposed system is to reduce the completion time of the task by increasing the speed. Cloud Sim environment tool kit is used for the testing of the proposed system.

Keywords:

Cloud computing,Task scheduling,GA (Genetic Algorithm),HGMWOA (Hybrid Genetic Modified Whale optimization algorithm),VM (Virtual Machine),

Refference:

I. A..Al-maamari and F.A. Omara.: ‘Task scheduling using hybrid algorithm in cloud computing environments’, Journal of Computer Engineering (IOSR-JCE), 17(3): p. 96-106, 2015. https://www.iosrjournals.org/iosr-jce/papers/Vol17-issue3/Version-6/N0173696106.pdf
II. A. S. Kumar and M. Venkatesan.: ‘Task scheduling in a cloud computing environment using HGPSO algorithm’, Cluster Computing, vol.22(6),p. 1-7, 2019. 10.1007/s10586-018-2515-2
III. Ahmed Y. Hamed, M. Kh. Elnahary and Hamdy H. El-Sayed.: ‘Task Scheduling Optimization in Cloud Computing by Jaya Algorithm’. Egypt Applied Science and Innovative Research. Vol. 7, No. 2, 2023. 10.22158/asir.v7n2p30
IV. C.T..Joseph, K. Chandrasekaran and R. Cyriac.: ‘A novel family genetic approach for virtual machine allocation’, Procedia Computer Science, vol.46, pp. 558-565, 2015. 10.1016/j.procs.2015.02.090
V. G. Jorge, C. Erik and A. Omar.: ‘Flower Pollination Algorithm for Multimodal Optimization’, Int. J.Comput. Intell. Syst., vol.10, pp.627–646, 2017. 10(1):627-646
VI. H. Hu, Y. Bai and T. Xu.: ‘A whale optimization algorithm with inertia weight’, WSEAS Trans. Comput., vol.15, pp.319-326, 2016. https://www.wseas.org/multimedia/journals/computers/2016/a545805-085.pdf
VII. H. Li and J. Zhang.: ‘Fast source term estimation using the PGA-NM hybrid method’, Eng. Appl.Artif. Intell., vol.62, pp.68–79,2017. 10.1016/j.engappai.2017.03.010
VIII. J. Yang, B. Jiang, Z. Lv and K. K. R. Choo.: ‘A task scheduling algorithm considering game theory designed for energy management in cloud computing’, Future Generation Computer Systems, vol. 105, pp. 985–992, 2020. https://doi.org/10.1016/j.future.2017.03.024
IX. Jia, LiWei, Kun Li and Xiaoming Shi.: ‘Cloud computing task scheduling model based on improved whale optimization algorithm’. Wireless Communications and Mobile Computing, 2021): 4888154. https://doi.org/10.1155/2021/4888154
X. M. H. Zhong and W. Long.: ‘Whale optimization algorithm based on stochastic adjustment control parameter’, Science Technology & Engineering, 2017.
XI. M. Ibrahim.: ‘Task scheduling algorithms in cloud computing: a review’. Turkish Journal of Computer and Mathematics Education, vol. 12, no. 4, pp. 1041–1053, 2021. 10.17762/turcomat.v12i4.612
XII. M. S. Sanaj and P. M. J. Prathap.: ‘An efficient approach to the map-reduce framework and genetic algorithm based whale optimization algorithm for task scheduling in cloud computing environment’. Materials Today Proceedings, vol. 37, pp. 3199–3208, 2021. 10.1016/j.matpr.2020.09.064
XIII. M.Agarwal and G.M.S. Srivastava.: ‘A Cuckoo Search Algorithm-Based Task Scheduling in Cloud Computing’, Advances in Computer and Computational Sciences, p. 293-299, 2018. 10.1007/978-981-10-3773-3_29
XIV. Majeed, MA Mushahhid and Sreehari Rao Patri.: ‘A hybrid of WOA and mGWO algorithms for global optimization and analog circuit design automation’, COMPEL-The international journal for computation and mathematics in electrical and electronic engineering, vol.38, pp.452-476, 2019. 10.1108/COMPEL-04-2018-0175
XV. N.Dordaie and N.J. Navimipour.: ‘A hybrid particle swarm optimization and hill climbing algorithm for task scheduling in the cloud environments’, ICT Express, 2017. 10.1016/j.icte.2017.08.001
XVI. P.K.Senyo, E. Addae and R. Boateng.: ‘Cloud computing research: A review of research themes, frameworks, methods and future research directions’, International Journal of Information Management, 38(1): p. 128-139, 2018. 10.1016/j.ijinfomgt.2017.07.007
XVII. R. Kaur and S. Kinger.: ‘Enhanced Genetic Algorithm based Task Scheduling in Cloud Computing’, International Journal of Computer Applications, vol. 101(14), 2014. DOI:10.5120/17752-8653
XVIII. R.S.Rathore, S.Sangwan, S.Mazumdar et al.,: ‘W-GUN: whale optimization for energy and delay-centric green underwater networks’, Sensors, vol. 20, no. 5, pp. 1377–1399, 2020. https://doi.org/10.3390/s20051377
XIX. S. H. Jang, T. Y. Kim, J. K. Kim and J. S. Lee.: ‘The study of genetic algorithm-based task scheduling for cloud computing’, International Journal of Control and Automation, vol. 5(4), pp. 157-162, 2012.C:/Users/ASUS/Downloads/2012.12 The Study of Genetic Algorithm-based Task Scheduling for Cloud Computing.pdf
XX. S. Ravichandran and D. E. Naganathan.: ‘Dynamic Scheduling of Data Using Genetic Algorithm in Cloud Computing’, International Journal of Computing Algorithm, vol. 2, pp. 127-133, 2013. 10.20894/IJCOA.101.002.001.003
XXI. S.A. Hamad, and F.A. Omara.: ‘Genetic-based task scheduling algorithm in cloud computing environment’, International Journal of Advanced computer Science and Applications, vol.7(4), p. 550-556, 2016.
XXII. T. Goyal and A. Agrawal.: ‘Host Scheduling Algorithm Using Genetic Algorithm In Cloud Computing Environment’, International Journal of Research in Engineering & Technology (IJRET), vol. 1, 2013. file:///C:/Users/ASUS/Downloads/–1372166085-2.%20Eng-Host%20Scheduling-Tarun%20Goyal%20(2).pdf
XXIII. W. Jing, C. Zhao, Q. Miao, H. Song and G. Chen.: ‘QoS-DPSO: QoS-aware task scheduling for cloud computing system’. Journal of Network and Systems Management, vol. 29, no. 1, pp. 1–29, 2021. https://doi.org/10.1007/s10922-020-09573-6
XXIV. W.Z. Sun and J.S.Wang.: ‘Elman neural network soft-sensor model of conversion velocity in polymerization process optimized by chaos whale optimization algorithm’, IEEE Access, vol.5, pp.13062- 13076, 2017. 10.1109/ACCESS.2017.2723610
XXV. X. Chen and D. Long.: ‘Task scheduling of cloud computing using integrated particle swarm algorithm and ant colony algorithm’, Cluster Computing, vol. 22 (4), pp. 2761–2769, 2019. DOI:10.1007/s10586-017-1479-y
XXVI. X. Chen, L. Cheng, C. Liu et al.,: ‘A WOA-based optimization approach for task scheduling in cloud computing systems’, IEEE Systems Journal, vol. 14, no. 3, pp. 3117–3128, 2020. 10.1109/JSYST.2019.2960088
XXVII. Y. Khalil, M. Alshayeji and I. Ahmad.: ‘Distributed Whale Optimization Algorithm based on Map Reduce’, Concurr. Comp. Pract. E., vol.31, 2019. https://doi.org/10.1002/cpe.4872
XXVIII. Zhihao Peng, Poria Pirozmand, Masoumeh Motevalli and Ali Esmaeili. : ‘Genetic Algorithm-Based Task Scheduling in Cloud Computing Using MapReduce Framework’. Mathematical Problems in Engineering, vol 4, pp.1-11, 2022. 10.1155/2022/4290382

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Abstract:

The dangers that Internet of Things (IoT) devices pose to large corporate corporations and smart districts have been dissected by several academics. Given the ubiquitous use of IoT and its unique characteristics, such as mobility and normalization restrictions, intelligent frameworks that can independently detect suspicious activity in privately linked IoT devices are crucial. The IoTs have led an explosion in traffic through the network, bringing information processing techniques for attack detection. The increase in traffic poses challenges in detecting attacks and differentiating traffic that is harmful. In this work, we have proposed a mechanism that uses the standard algorithms in a system that is designed to detect, track, measure and identify online traffic from organizations with malignant transmission: Random Forest (RF), gradient-boosted decision trees (GBDT), and support vector machines (SVM) gives an optimal accuracy of 80.34%,87.5%, and 88.6% while the random forest-based supervised approach is 5.5% better than the previous techniques. To facilitate comparisons between training time, prediction time, specificity, and accuracy, the proposed approach leverages the NSL KDD dataset accuracy.

Keywords:

NSL-KDD dataset distribution,IoT Security,Fog Computing,Deep Learning,Random Forest (RF) machine learning,

Refference:

I. Asish Mitra, Numerical Simulation Of Laminar Convection Flow And Heat Transfer At The Lower Stagnation Point Of A Solid Sphere., J. Mech. Cont.& Math. Sci., Vol.10, No.1, Pp 1469-1480, 2015.
II. A. Belabed, E. Aïmeur And A. Chikh, “A Personalized Whitelist Approach For Phishing Webpage Detection”, 2012 Seventh International Conference On Availability, Reliability And Security, Prague, Pp. 249-254, 2012.
III. A. Naz, H. Khan, I. U. Din, A. Ali, M. Husain, “An Efficient Optimization System for Early Breast Cancer Diagnosis based on Internet of Medical Things and Deep Learning”, Engineering, Technology & Applied Science Research, Vol.14, No.4, pp. 15957-15962, 2024.
IV. Hassan, H. Khan, I. Uddin, A. Sajid, “Optimal Emerging trends of Deep Learning Technique for Detection based on Convolutional Neural Network”, Bulletin of Business and Economics (BBE), Vol.12, No.4, pp. 264-273, 2023.
V. H. Khan, A. Ali, S. Alshmrany, “Energy-Efficient Scheduling Based on Task Migration Policy Using DPM for Homogeneous MPSoCs”, Computers, Materials & Continua, Vol.74, No.1, pp. 965-981, 2023.
VI. H. Sarwar, H. Khan, I. Uddin, R. Waleed, S. Tariq, “An Efficient E-Commerce Web Platform Based on Deep Integration of MEAN Stack Technologies”, Bulletin of Business and Economics (BBE), Vol. 12, No.4, pp. 447-453, 2023.
VII. Hammad. A , E. Zhao, “Mitigating link insecurities in smart grids via QoS multi-constraint routing“, In 2016 IEEE International Conference on Communications Workshops (ICC)”, pp. 380-386. 2016.
VIII. H. Khan, I. Uddin, A. Ali, M. Husain, “An Optimal DPM Based Energy-Aware Task Scheduling for Performance Enhancement in Embedded MPSoC” Computers, Materials & Continua, Vol.74, No.1, pp. 2097-2113, 2023.
IX. Hammad, A. A., Ahmed, “Deep Reinforcement Learning for Adaptive Cyber Defense in Network Security”, In Proceedings of the Cognitive Models and Artificial Intelligence Conference, pp. 292-297, 2016.
X. H. Khan, M. U. Hashmi, Z. Khan, R. Ahmad, “Offline Earliest Deadline first Scheduling based Technique for Optimization of Energy using STORM in Homogeneous Multi-core Systems,” IJCSNS Int. J. Comput. Sci. Netw. Secur, Vol.18, No.12, pp 125-130, 2018.
XI. Hossein Shirazi, Bruhadeshwar. B,”Kn0w Thy Doma1n Name”: Unbiased Phishing Detection Using Domain Name Based Features. In Proceedings Of The 23nd Acm On Symposium On Access Control Models And Technologies (Sacmat ’18). Association For Computing Machinery, New York, Ny, Usa, pp. 69-75, 2018.
XII. Hussain, S., Rajput, U. A., Kazi, Q. A., & Mastoi, S, “Numerical investigation of thermohydraulic performance of triple concentric-tube heat exchanger with longitudinal fins”, J. Mech. Cont. & Math. Sci, Vol. 16, No. 8, pp 61-73, 2021.
XIII. H. Khan, S. Ahmad, N. Saleem, M. U. Hashmi, Q. Bashir, “Scheduling Based Dynamic Power Management Technique for offline Optimization of Energy in Multi Core Processors” Int. J. Sci. Eng. Res, Vol.9, No.12, pp 6-10, 2018.
XIV. H. Khan, K. Janjua, A. Sikandar, M. W. Qazi, Z. Hameed, “An Efficient Scheduling based cloud computing technique using virtual Machine Resource Allocation for efficient resource utilization of Servers” In 2020 International Conference on Engineering and Emerging Technologies (ICEET), IEEE, pp 1-7, 2020.
XV. Hammad, M., Jillani, R. M., Ullah, S., Namoun, A., Tufail, A., Kim, K. H., & Shah, H, “Security framework for network-based manufacturing systems with personalized customization”, An industry 4.0 approach, Sensors, vol. 23. No. 17-55, 2022.
XVI. H. Khan, Q. Bashir, M. U. Hashmi, “Scheduling based energy optimization technique in multiprocessor embedded systems” In 2018 International Conference on Engineering and Emerging Technologies (ICEET), IEEE, pp 1-8, 2018.
XVII. H. Khan, A. Yasmeen, S. Jan, U. Hashmi, “Enhanced Resource Leveling Indynamic Power Management Techniqueof Improvement In Performance For Multi-Core Processors”, Journal Of Mechanics Of Continua And Mathematical Sciences, Vol.6, No.14, pp. 956-972, 2019.
XVIII. H. Khan, K. Janjua, A. Sikandar, M. W. Qazi, Z. Hameed, “An Efficient Scheduling based cloud computing technique using virtual Machine Resource Allocation for efficient resource utilization of Servers” In 2020 International Conference on Engineering and Emerging Technologies (ICEET), IEEE, pp 1-7, 2020.
XIX. H. Huang, J. Tan And L. Liu, “Countermeasure Techniques For Deceptive Phishing Attack”, International Conference On New Trends In Information And Service Science, Beijing, pp. 636-641, 2009.
XX. H. Khan, M. U. Hashmi, Z. Khan, R. Ahmad, “Offline Earliest Deadline first Scheduling based Technique for Optimization of Energy using STORM in Homogeneous Multi-core Systems” IJCSNS Int. J. Comput. Sci. Netw. Secur, Vol.18, No.12, pp 125-130, 2018.
XXI. H. Khan, M. U. Hashmi, Z. Khan, R. Ahmad, A. Saleem, “Performance Evaluation for Secure DES-Algorithm Based Authentication & Counter Measures for Internet Mobile Host Protocol” IJCSNS Int. J. Comput. Sci. Netw. Secur, Vol.18, No.12, pp 181-185, 2018.
XXII. J. Chen; J. Tan, C. Chang, F. Feng, “A New Cost-Aware Sensitivity-Driven Algorithm for the Design of FIR Filters”, IEEE Transactions on Circuits and Systems I, Vol. 64, No. 6 pp: 1588 – 1598, 2017.
XXIII. M. Y. A. Khan, F. Khan, H. Khan, S. Ahmed, M. Ahmad, “Design and Analysis of Maximum Power Point Tracking (MPPT) Controller for PV System” Journal of Mechanics of Continua and Mathematical Sciences, Vol.14, No.1, pp 276-288, 2019.
XXIV. M. Y. A. Khan, “A GSM based Resource Allocation technique to control Autonomous Robotic Glove for Spinal Cord Implant paralysed Patients using Flex Sensors”, Sukkur IBA Journal of Emerging Technologies, Vol.3, No.2, pp 13-23, 2020.
XXV. M. Y. A. Khan, “A high state of modular transistor on a 105 kW HVPS for X-rays tomography Applications”, Sukkur IBA Journal of Emerging Technologies, Vol.2, No.2, pp 1-6, 2019.
XXVI. M. Shah, S. Ahmed, K. Saeed, M. Junaid, H. Khan, “Penetration testing active reconnaissance phase–optimized port scanning with nmap tool” In 2019 2nd International Conference on Computing, Mathematics and Engineering Technologies (iCoMET), IEEE, pp 1-6, 2019.
XXVII. M. Y. A. Khan, M. Ibrahim, M. Ali, H. Khan, E. Mustafa, “Cost Benefit Based Analytical Study of Automatic Meter Reading (AMR) and Blind Meter Reading (BMR) used by PESCO (WAPDA),” In 2020 3rd International Conference on Computing, Mathematics and Engineering Technologies (iCoMET), IEEE, pp 1-7, 2020.
XXVIII. M. Y. A. Khan, “Enhancing Energy Efficiency in Temperature Controlled Dynamic Scheduling Technique for Multi Processing System on Chip” Sukkur IBA Journal of Emerging Technologies, Vol.2, No.2, pp 46-53,2019.
XXIX. M. U. Hashmi, S. A. ZeeshanNajam, “Thermal-Aware Real-Time Task Schedulabilty test for Energy and Power System Optimization using Homogeneous Cache Hierarchy of Multi-core Systems” Journal of Mechanics of Continua and Mathematical Sciences, Vol.14, No.4, pp 442-452, 2023.
XXX. M. Y. A. Khan, U. Khalil, H. Khan, A. Uddin, S. Ahmed, “Power flow control by unified power flow controller” Engineering, Technology & Applied Science Research, Vol.9, No.2, pp 3900-3904, 2019.
XXXI. R. Waleed, A. Ali, S. Tariq, G. Mustafa, H. Sarwar, S. Saif, I. Uddin, “An Efficient Artificial Intelligence (AI) and Internet of Things (IoT’s) Based MEAN Stack Technology Applications” Bulletin of Business and Economics (BBE), Vol.13, No.2, pp 200-206, 2024.
XXXII. S. Khan, I. Ullah, M. U. Rahman, H. Khan, A. B. Shah, R. H. Althomali, M. M. Rahman, “Inorganic-polymer composite electrolytes: basics, fabrications, challenges and future perspectives” Reviews in Inorganic Chemistry, Vol.44, No.3, pp 1-29, 2024.
XXXIII. S. Khan, I. Ullah, H. Khan, F. U. Rahman, M. U. Rahman, M. A. Saleem, A. Ullah, “Green synthesis of AgNPs from leaves extract of Salvia Sclarea their characterization, antibacterial activity and catalytic reduction ability” Zeitschrift für Physikalische Chemie, Vol.238, No.5, pp 931-947, 2024.
XXXIV. T. M. Gondal, Z. Hameed, M. U. Shah, H. Khan, “Cavitation phenomenon and its effects in Francis turbines and amassed adeptness of hydel power plant” In 2019 2nd International Conference on Computing, Mathematics and Engineering Technologies (iCoMET), IEEE, pp 1-9, 2019.

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Abstract:

This paper aims to study the flow of a non-Newtonian fluid of Reiner-Rivlin type between two co-axial porous circular cylinders. The inner cylinder moves with a transient velocity while the outer one is fixed.

Keywords:

Co-axial Porous,Non-Newtonian fluid,Transient Velocity,

Refference:

I. Bagchi, K. C. : Appl. Sci. Ros., 16, 131, 1966.
II. Goutam Chakraborty & Supriya Panja. : ‘ON THE FLOW OF TWO IMMISCIBLE VISCO-ELASTIC FLUIDS THROUGH A RECTANGULAR CHANNEL’. J. Mech. Cont. & Math. Sci. Vol. 10(1), pp. 1464-1448. 10.26782/jmcms.2015.10.00003
III. Khamrui, S. R. : Ball. Cal. Math. Soc., 25, 45, 1950.
IV. Rivlin, R. S. : Proc. Roy. Soc. Lond., 193, 260, 1948.
V. Rukhsar Khatun, Goutam Chakraborty, Md Sadikur Rahman. : ‘OPTIMAL POLICY OF THE INTERVAL EPQ MODEL USING C-L INTERVAL INEQUALITY’. J. Mech. Cont. & Math. Sci. Vol. 18(12), pp. 20-31, 2023. 10.26782/jmcms.2023.12.00002
VI. Sommerfeld, A. : Partial Differential Equations in Physics., New York.
VII. Watson, G. N. : ‘Theory of Bessel Functions.

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